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Cel

The aim of the project is to study new problems of algebraic and analytic geometry with emphasis on D-modules and moduli spaces of G-bundles, as well as related problems of infinite-dimensional groups, quantum groups, and their applications.

The purpose is : to construct and study natural families of D-modules on G-bundles on a smooth projective curve and to clarify their relation to Langlands' program; to develop an algebraic-geometric formalism for operator product expansion in conformal field theory; to study geometric realisations of representations of quantum groups as D-modules on configuration spaces; to study homogeneous spaces of quantum groups and PoissonLie groups; and to study index formulae and integral transformations such as the Penrose transform using D-module theory.